Browsing by Author "Khater, A. H."

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On Vladimirov’s approximation for ideal in homogeneous MHD
(2005-08) Callebaut, D. K.; Karugila, G. K.; Khater, A. H.
Vladimirov and Vladimirov and Moffat have considered configurations in ideal magnetohydrodynamics, i.e. inviscid and perfectly conducting. The matter is considered as incompressible. However, the density is allowed to vary slowly. They base the following approximation on this slow variation: they omit the mass density in front of the total derivative of the velocity in the equation of motion. Normally the mass density should appear in front of Du. This is a tremendous simplification which allows them to obtain various interesting results concerning the stability of the configurations. However, in such a kind of approximation the results might be only crude. However, in many applications the results are OK, because crucial in those papers is the vanishing of ∇ρ × ∇φ. Often both gradients are parallel and the results obtained by Vladimirovs approximation are nevertheless valid, e.g. in the application to inhomogeneous gas clouds and protostars. Moreover for small density gradients and/or nearly parallel gradients the approximation is fair. We even suggest an approximation which may be more correct and avoids the term ∇ρ × ∇φ. Hence for linear perturbations and stability analyses the results may turn out to be acceptable. However, for nonlinear stability a more extended analysis is required.